we find that the only solution consistent with the boundary conditions is \(W(x)=U(x)\equiv 0\) , i.e. no deformation. However, for \(\epsilon \ge \epsilon ^\star \) , we find a non-trivial, uniformly periodic wrinkling solution for the vertical displacement; the wavelength of wrinkling is \(\lambda =(B/K)^{1/4}\) , consistent with previous reports [1]}, [2]}. Thus, analysis of the linearized equations implies a bifurcation point when \(\epsilon =\epsilon ^\star \)  (Fig. REF (b)). The physical interpretation of \(\epsilon ^\star \)  is the maximal amount of strain that can be accommodated by filament stretching (compression) without causing any bending and spring deformation. Indeed, \(\epsilon ^\star \)  is inversely proportional to \(S\) ; decreasing \(S\)  leads to a higher strain threshold \(\epsilon ^\star \) . Above the critical swelling/growth strain \(\epsilon ^\star \) , the excess strain \(\epsilon -\epsilon ^*\)  is accommodated by filament buckling.
